What's the physical basis for a memristor?

The NY Timesreports today that Hewlett-Packard has succeeded in fabricating the memristor predicted by Leon Chua in 1971:

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The original theoretical work done by Mr. Chua was laid out in a paper, “Memristor — The Missing Circuit Element.” The paper argued that basic electronic theory required that in addition to the three basic circuit elements — resistors, capacitors and inductors — a fourth element should exist.

I understand the physical basis of resistors, capacitors and inductors, more or less. School me on Chua's paper.

As to my understanding of basic circuit elements, DC circuits are pretty much identical to systems of water pipes, tanks (and valves), where a resistor is analogous to pipe friction and capacitors are analogous to water tanks or the capacitance of a wire. Inductors add a new dimension to electrical circuits not analogous to water systems by storing energy in magnetic fields. I would guess that the memristor might be adding still another dimension by storing energy in some sort of field with which I'm not familiar.

The device scales to 4 nm, which is close to atomic size, but unfortunately may be 10x slower than DRAM. It also apparently can hold more than two states, which might enable circuit-level simulation of biological neuron circuits. It also appears useful for programmable logic arrays.

The proposed 'memristor' changes its impedance depending on the current applied. At any given instant, a 'memristor' is a resistor, where V=IR. However, the application of I will change R accordingly.

A 'memristor' may be in either direction, it could undergo runaway, where R(m) reduces as I increases, or it do the opposite and increase R(m) as I increases. This is all trivial to implement by anyone with half a clue, but the proper 'memristor' will not 'forget' what R(m) it was last week, last year after I has been removed; Memristors are non-volatile.

They are analog devices in that R(m) can equal any value but will periodically need refreshing if they're used for storage, since sensing the current impedance (I crack myself up) would require the passing of a current.

The applications for digital memory seem pretty straight forward (bits stored as high/low resistance), but since reading about this yesterday I've been trying to figure out how it would fit into standard linear circuits.

If we could imagine what a university electric circuits class would be like say 10 years from now assuming this became a standard electronic device, what would be the canonical RLCM circuit? (Would there be one?)

Wikipedia is the only place I've seen some math attached to the hype, giving M(q)=dΦe/dq and V(t)=M(q(t))I(t). I'm not sure how to fit that into standard circuit theory. Maybe it's just because I don't have any kind of intuitive way to understand a memristor at the moment.

(Side note, I think the water analogy of electric circuits leads to more problems than it solves. Basic circuit theory isn't hard to explain to someone who can understand high school physics, provided you don't muck it up with pipes and tanks. )

Originally posted by Hat Monster:A 'memristor' may be in either direction, it could undergo runaway, where R(m) reduces as I increases, or it do the opposite and increase R(m) as I increases. This is all trivial to implement by anyone with half a clue, but the proper 'memristor' will not 'forget' what R(m) it was last week, last year after I has been removed; Memristors are non-volatile.

It's not current that is the relevant quantity to a memristor, but charge (current integrated over the lifetime of the device). We already have devices which change their resistance as a function of current. One example is a lightbulb, where the resistance goes up with increasing current due to filament heating. A second is silicon carbide, which has a high resistance at room temperature that decreases with current, again due to filament heating.

A memristor is different in that its resistance is proportional to the total charge that has passed through it, with current in one direction increasing the resistance and current in the other decreasing it. Current dependent resistors work the same way in both directions.

Basic circuit theory isn't hard to explain to someone who can understand high school physics, provided you don't muck it up with pipes and tanks.

As a personal anecdote, the water analogy never made sense to me until I understood the physics behind circuits - then it suddenly seemed like a decent teaching tool

I can't really think of a good simple representation using water analogies, but I suppose you could use a pipe with a variable diameter that's geared by a small water wheel/turbine in the pipe - ie, the water through the pipe turns the wheel and cinches the pipe towards open/closed (depending on the sign of M). Basically, the volume of water that's flowed past the wheel determines the size of the pipe. Or some reasonable facsimile thereof .

Edit: I suppose I should post this in the comments on Ethan's article, but his discussion of the magnetic field dependence left me initially baffled - the description on Wikipedia (and Nekko's) are far more simple.

Once I had a large irrigation system to manage, it helped my understanding of circuits! Electrons=water; capacitance=a tank; resistance=frictional loss in a pipe. I'm not sure about inductance, as I said; for one thing, it has no analogy in plumbing.

The analogy was first presented to me during E&M, and made no sense to me. I wasn't used then to thinking about science in terms of objects in the real world, so even a description of an experiment during a lecture often went sailing right over my head.

So a memister is like a pipe made of some porous material inside, rather than hollow, which gradually soaks up water when it flows one way, impeding further flow, while flow the other way clears out the clogging water? Sounds like a semiconductor where the holes fill up or empty depending on the polarity.

Not too dissimilar to a transistor, except there are only two wires; no independent way to turn the valve on or off or up and down.

Virotheconq, Would you please provide a link to the article by Ethan that you referenced. TIA

The EETimes article also has some interesting comments/perspective by Dr. Chua.

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So a memister is like a pipe made of some porous material inside, rather than hollow, which gradually soaks up water when it flows one way, impeding further flow, while flow the other way clears out the clogging water? Sounds like a semiconductor where the holes fill up or empty depending on the polarity.

That analogy works too, but I imagine such a sponge would be made from unobtanium. And yes, this memristor (my inner spelling freak weeps) works by essentially moving O vacancies (not electrical holes) between two layers of a TiO2 thin film, which changes the conductance of the layers.

Once I had a large irrigation system to manage, it helped my understanding of circuits! Electrons=water; capacitance=a tank; resistance=frictional loss in a pipe. I'm not sure about inductance, as I said; for one thing, it has no analogy in plumbing.

Except that in standard circuit theory electrons would flow the opposite direction of the water, the capacitor-as-a-tank starts to break down as soon as you move away from basic DC, and lacking an analog for inductance is a pretty big omission.

I usually try to explain passive circuits through basic laws of current flow through conductors. Resistance, inductance, and capacitance are just properties of conductors in different configurations, which cause certain electromagnetic effects to become dominant. Resistance is a property of every conductor, two conductors next to each other form a capacitor, and a conductor twisted into a loop is an inductor.

I'm not sure how a memristor would fit into that framework. It looks like their construction is closer to that of an active silicon device.

So, in water-analogy terms, a memristor would be be like a river. It can carve out a huge canyon (increased R value) but if that river were reversed, it could fill that canyon with silt. (decreased R value).

The hold-up over the last 37 years, according to professor Chua, has been a misconception that has pervaded electronic circuit theory. That misconception is that the fundamental relationship in passive circuitry is between voltage and charge. What the researchers contend is that the fundamental relationship is actually between changes-in-voltage, or flux, and charge. Such is the insight that enabled HP to invent the memristor, according to Chua and Williams.

"Electronic theorists have been using the wrong pair of variables all these years--voltage and charge. The missing part of electronic theory was that the fundamental pair of variables is flux and charge," said Chua. "The situation is analogous to what is called "Aristotle's Law of Motion, which was wrong, because he said that force must be proportional to velocity. That misled people for 2000 years until Newton came along and pointed out that Aristotle was using the wrong variables. Newton said that force is proportional to acceleration--the change in velocity. This is exactly the situation with electronic circuit theory today. All electronic textbooks have been teaching using the wrong variables--voltage and charge--explaining away inaccuracies as anomalies. What they should have been teaching is the relationship between changes in voltage, or flux, and charge."

Williams (the inventor of the device) goes on to say that he did it by considering the relationship of flux and charge. Those are extremely strong words from Chua, BTW. It seems he's right; if so, I would expect a Nobel to him and Williams for this work.

I'm still completely in the black as to what this voltage/mag-flux relationship is and how that relates to the device, and what relates a "flux" in voltage to a "flux" in a mag field? I didn't bother paying to read the Nature article, not that it was likely I would understand it. Might dig back into Chua's work (not likely I'll understand that either).

My mention of holes related to npn transistors or diodes, where the current can be carried by holes or electrons, IIRC from 25 years ago. Wouldn't the absence of the oxygen molecule be a hole?

Holes in an electrical context are (at a high level) the absence of an electron. In certain perspectives (like your semiconductor example), they can be treated as a mobile positive charge. While the absence of an oxygen (atom, not molecule, was my interpretation) could be considered a "hole" in a layman's perspective, it isn't using this definition.

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I'm still completely in the black as to what this voltage/mag-flux relationship is and how that relates to the device, and what relates a "flux" in voltage to a "flux" in a mag field?

A flux is basically the "amount" of a field going through a defined surface, and voltage is not a field, so there is no such thing as a voltage flux. AFAICT, there is no relationship between magnetic fields and electrical potential in this application - it has more to do with net charge passed through the memristor.

Having read through the Nature article on the memristor, here's my attempt at describing the kind of device that can be considered a memristor:

Take a very thin semiconductor membrane (thickness D is in nanomemeteres), and attach an contact on the top and bottom sides.

This, by itself, is just a resistor - the current through the membrane is a function of the resistivity of the semiconductor and the thickness D. The resistivity is a function of various properties of the semiconductor (electron drift rate, etc).

To make a memristor, the film is doped partway through with ions, which change the conductivity of the film, but only in the section that contains the ions.

So now you have two resistors in series, Ron and Roff. Ron is the doped section of the film, with low resistance. Roff is the rest of the film, with high resistance. The average resistivity is now a weighted sum of the resistivities of the two sections.

The clever thing is, once you pass current through this device, the ions migrate (unclear to me if new ions are create, as well), and the width of the two regions change, and therefore the resistance changes.

So pass in a positive current, the ions move to increase the thickness of the Ron region->resistance goes down. Pass in a negative current, the ions move back, the resistance goes up.

Why hasn't anyone noticed this before? Because the size of the effect scales as 1/D^2, and only becomes appreciable once D, the film thickness, reaches nanoscale.

It's nice that this apparently also explains a lot of strange hysteresis/negative resistance effects that appear in nanoscale devices.

Originally posted by Virogtheconq:Holes in an electrical context are (at a high level) the absence of an electron. In certain perspectives (like your semiconductor example), they can be treated as a mobile positive charge. While the absence of an oxygen (atom, not molecule, was my interpretation) could be considered a "hole" in a layman's perspective, it isn't using this definition.

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I'm still completely in the black as to what this voltage/mag-flux relationship is and how that relates to the device, and what relates a "flux" in voltage to a "flux" in a mag field?

A flux is basically the "amount" of a field going through a defined surface, and voltage is not a field, so there is no such thing as a voltage flux. AFAICT, there is no relationship between magnetic fields and electrical potential in this application - it has more to do with net charge passed through the memristor.

I always thought voltage was potential, which creates an electric field, and then moving charges create a magnetic field, but I'd have to go 30 years back to dust off those E&M equations beyond V=iR to know the difference between a field and a potential. I read Chou's quote as saying it's changes in field strength, which he called flux, that are important. The missing symmetry is reported on the Ars front page as between a magnetic field and charge.

Gotcha on a traditional npn-transitor hole being in the electron shell and here they're talking about the whole ion moving around the crystal, nucleus and all. And is it O or O2 that has a magnetic moment?

Oh, and the whole water analogy collapses as soon as you introduce magnetism, which is not a property of water. Magnetism appears to be involved here.

Voltage is potential, which is a line integral of a vector field - ie, the sum of the vectors along a particular path. Flux is a surface integral - the sum of all the vectors through a surface. For a constant surface, a change in flux could result in a change in potential, as it implies the field is changing.

I don't quite understand what Chua is saying, either, but I'm also several years rusty on my E&M. I'm guessing there's also some semantic differences in EE-speak due to implicit relationships in electromagnetism that they deal with on a day-to-day basis.

Originally posted by shread:Once I had a large irrigation system to manage, it helped my understanding of circuits! Electrons=water; capacitance=a tank; resistance=frictional loss in a pipe. I'm not sure about inductance, as I said; for one thing, it has no analogy in plumbing.

The analogy was first presented to me during E&M, and made no sense to me. I wasn't used then to thinking about science in terms of objects in the real world, so even a description of an experiment during a lecture often went sailing right over my head.

The fluid inertia is the liquid system analog to inductance. Inductance resists changes in current. Fluid inertia resists changes in flow. There is also the mass, spring, dashpot analog to circuits or fluid systems.

Thinking of what happens when you grow a ferromagnet on top of an antiferromagnet, this really seems pretty obvious. I'm surprised it took this long to observe the effect, especially since people have been growing nanoscale films for decades.

Originally posted by JasonF:Thinking of what happens when you grow a ferromagnet on top of an antiferromagnet, this really seems pretty obvious. I'm surprised it took this long to observe the effect, especially since people have been growing nanoscale films for decades.

I'm not a nanotech person, but as far as I can tell from the writeups on this, these effects have in fact been often observed in nanostructures.

But since they were unexpected, it's just been inexplicable hysteresis, negative apparent resistance, and so on, and one of the contributions of this work is to explain what might be going on with all that. And since it appears the mechanism can lead to very different qualitative circuit behavior depending on input stimulus and the device structure, the unexpected behaviors in nanostructures have been various and hard to theorize about.

Originally posted by shread:Once I had a large irrigation system to manage, it helped my understanding of circuits! Electrons=water; capacitance=a tank; resistance=frictional loss in a pipe. I'm not sure about inductance, as I said; for one thing, it has no analogy in plumbing.

The analogy was first presented to me during E&M, and made no sense to me. I wasn't used then to thinking about science in terms of objects in the real world, so even a description of an experiment during a lecture often went sailing right over my head.

The fluid inertia would seem to be the liquid-system analog to inductance. Inductance resists changes in current. Fluid inertia resists changes in flow. There is also the mass, spring, dashpot analog to circuits or fluid systems.

Electrons have mass. That's their inertia, it's just negligible. If you spin up a magnetic field in an inductor and then cut the circuit, a lot of juice flies out of that magnetic field as it collapses. I can't think of any analogy to that closer than opening a raised water tank, but my guess is that the gravity field associated with that is more akin to a voltage than a magnetic field. The momentum transferred to you from water from a fire hose probably has some analogy in E&M, but, again, I would guess that the mass of an electron is negligible in most systems.

It was depressing to realize that it's 36 years since I took E&M, not 30.

Originally posted by shread:Once I had a large irrigation system to manage, it helped my understanding of circuits! Electrons=water; capacitance=a tank; resistance=frictional loss in a pipe. I'm not sure about inductance, as I said; for one thing, it has no analogy in plumbing.

The analogy was first presented to me during E&M, and made no sense to me. I wasn't used then to thinking about science in terms of objects in the real world, so even a description of an experiment during a lecture often went sailing right over my head.

The fluid inertia would seem to be the liquid-system analog to inductance. Inductance resists changes in current. Fluid inertia resists changes in flow. There is also the mass, spring, dashpot analog to circuits or fluid systems.

Electrons have mass. That's their inertia, it's just negligible. If you spin up a magnetic field in an inductor and then cut the circuit, a lot of juice flies out of that magnetic field as it collapses. I can't think of any analogy to that closer than opening a raised water tank, but my guess is that the gravity field associated with that is more akin to a voltage than a magnetic field. The momentum transferred to you from water from a fire hose probably has some analogy in E&M, but, again, I would guess that the mass of an electron is negligible in most systems.

It was depressing to realize that it's 36 years since I took E&M, not 30.

Electron inertia is not a factor in lumped parameter circuit analysis. Inductance and mass/inertia are direct analogs in lumped parameter systems analysis. If you trip a pump in a closed fluid circuit the momentum (inertia) in the liquid does not allow the flow to stop instantaneously. The flow coasts down to a stop similarly to what an inductor does in an electric circuit. Gravity from a raised water tank would be the analog to a capacitor in an electric circuit. The pressure difference in a fluid system is the analog to a voltage difference in a circuit. Pressure is the fluid potential. Voltage is the electric potential.

^^^^ The inertia in the water may behave the same mathematically as inductance, but it's not directly comparable physically. Conceptually, to me, there's no difference between an electron sitting on the negative pole of a battery right before it's switched on, and a drop of water at the edge of a cliff. Likewise, the inertia of a drop is directly comparable to that of an electron, except that inertia is negligible for electrons because of their small mass. Inductance, on the other hand, has no direct analogue, in my mind, in, err, plumbing.

Originally posted by shread:^^^^ The inertia in the water may behave the same mathematically as inductance, but it's not directly comparable physically. Conceptually, to me, there's no difference between an electron sitting on the negative pole of a battery right before it's switched on, and a drop of water at the edge of a cliff. Likewise, the inertia of a drop is directly comparable to that of an electron, except that inertia is negligible for electrons because of their small mass. Inductance, on the other hand, has no direct analogue, in my mind, in, err, plumbing.

It is just a dynamical systems analog. There is no direct physics analog between the two. In an electrical circuit the energy (1/2 Li**2) is stored in the magnetic field of the inductor and in the plumbing system the energy (1/2 mv**2) is stored in the kinetic energy of the liquid.

EDIT: The only direct analog I can think of would be if you added a turbine connected to a flywheel in the fluid system where the fluid inertia was negligible. The flywheel would spin up with the flow and transfer energy back to the fluid if the flow decreased. The energy would be stored in the mechanical energy of the flywheel.

Not to get too loungy or soapboxy, but isn't this kind of exciting? When people say, "You have no idea how the century will turn out," I tend to nod in agreement, but part of me doubts that there will ever be any new fundamental developments. I mean, sure, I can guess on faster and denser everythings, but I have a hard time imagining someone coming up with entire new stuff.

And what have we found in one week? Memristors and Eka-thorium. And better than eka-thorium is a manner in which to search for other previously unheard of atomic numbers. And I love the fact that we're debating the physical analog of memristors -- it shows truly how foreign they are to our thinking, which could mean for some really wild inventions in the next couple of decades.

I still don't understand memristor, but I have to comment on the water analogy.

I always preferred the more direct sound explanation. Explain how a dynamic microphone works and you get the speaker for free... then explain how the basic circuit elements affect sound. Most people already understand the bass/treble knobs on their stereo, plus it gets them primed for Fourier analysis. Try explaining THAT with water! (hrm... well air is a fluid too...)

Maybe somebody smarter than I can explain the effect of a memristor on sound.

Originally posted by Unrated:Do you think we'll ever be able to get our hands on a memristor (in a convenient 2-lead surface mount package), or are these destined to stay in the realm of integrated devices and specialty circuits?

Given that the effect described here requires a nanostructure, probably not, unless someone puts a single one in a macroscale package.

Originally posted by LordFrith:Not to get too loungy or soapboxy, but isn't this kind of exciting?

Last night I was reading Chua's original 1971 paper and caught myself idly wondering where on the EE pantheon should be placed. A new passive component automatically places the result as more fundamental than anything after the heralding of the digital age by Shannon. In terms of novelty and potential applicability, intuitively seems right to peg this somewhere around the advent of radio.

Well, a memristor should not, for the most part, effect sound I think.

I think of it this way, you have a crystal which will pass current in both directions, however as current flows through it it creates chemical reactions that increase the resistance until it won't pass any current. The only way to reverse the chemical reaction is to reverse the current. The resistance then goes from infinity back to zero, and if you keep the current flowing in reverse it'll go back to infinity.

If you stop at any time it has a memory in its chemical structure (resistance) that indicates the sum of current that has flowed through it.

So you can use it to store information (use a circuit that sets the resistance to 0, or 1 ohms, or say 0 - 4 ohms and make it store 2 bytes...). To read you simply use an alternating current to read the resistance without flowing a net current through it.

I also gather that for a while people were looking for these things in such a manner that the resistance would be due to magnetic fields (since its a device that operates on magnetic flux and current)... But the ones they've found are chemical.

The OP specifically mentioned his knowledge of DC circuits and the water analogy. You're describing currents going "back and forth", which suggests you need to understand frequency space. It's nice that the RLC circuit model fits into a linear 2nd order diff eq, which can be easily interpreted if you know that microphones turn sound into voltage fluctuations.

I think you're describing an operation that would have a frequency-dependent effect, but it definitely doesn't sound linear.

Still reading about this, and the more I read, the more promising this technology seems. Here's an analogy I've dug up while trying to wrap my mind around this startling find.

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from the IEEE SpectrumThe classic analogy for a resistor is a pipe through which water (electricity) runs. The width of the pipe is analogous to the resistance of the flow of current—the narrower the pipe, the greater the resistance. Normal resistors have an unchanging pipe size. A memristor, on the other hand, changes with the amount of water that gets pushed through. If you push water through the pipe in one direction, the pipe gets larger (less resistive). If you push the water in the other direction, the pipe gets smaller (more resistive). And the memristor remembers. When the water flow is turned off, the pipe size does not change.

The device begins in the off position, with the layer of insulating titanium dioxide blocking current. But when the researchers apply a positive voltage to one of the metal contacts, the oxygen atoms move from one titanium dioxide layer to the other; as a result, oxygen vacancies exist in both layers. "When that happens, the resistance of the material drops dramatically," Williams says, allowing current to flow through the device. "We've actually built devices where the resistance of the device changes by six orders of magnitude."

With a gain like that, a circuit designer could cram the functionality of an entire operational amplifier onto a single crossbar intersection - an area on the order of 2.89*10^-4 square microns (using 17nm for a single strand). Additionally, the crossbar would allow thousands of inputs and outputs - something impossible to do with current VLSI assumptions. By way of comparison, the limit of the so-called "fan out" is 4 for various technical reasons that I don't understand fully.

For a sense of scale in the complexity, here's picture of an op-amp I've d/l from the Wiki to help make my point:

It's an easy next step to imagine these strands of TiO2 as an interconnect for a "sea of logic". Given its favorable characteristics, such as the high-gain, extremely large fan-in/fan-out, the network of devices on a hybrid chip takes on something eerily similar in topology and performance to the human brain:

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HP researchers are also making memristor-based chips that mimic the workings of neural networks in the brain. During learning, the connections between neurons in the brain change, some becoming stronger and others weaker over time. The strength of these connections can have a range of different values. It's possible to simulate this range by making circuits of many transistors. But this can take a large number of transistors. Williams says that it's possible to do the same thing with just one memristor, since it can be set to have a range of different resistance levels. That could reduce the size of such neural networks by 10,000 times, he says.

Mathematically, it's pretty trivial. It's a two terminal passive component that changes the magnetic flux between the terminals as a function of the amount of electric charge that has passed through the device. As such, because it is able to produce the linear behavior of a resistor with a constant current, I think it's a generalization and, as such, will replace it as a fundamental passive element. Still leaving the EE's with three, then.

But I suspect you meant, what does it mean physically? Well, that's a bit harder. Since its behavior can't be reproduced within an RLC network, it's hard to come up with analogies that work. That's part and parcel to it being fundamental, after all.

One way of looking at the thing is to imagine skipping rocks into a pond. Further imagine the rock as the charge and the total motion of the waves against the edges of the pond as the total current applied. You can choose to keep the resistance the same by keeping the size of the rock and the velocity constant. You can also choose to vary the resistance by choosing a bigger rock, but that will still yield the same flux per unit of charge. What the spontaneous action of a memristor looks like is throwing the same size rock at different velocities, thereby giving a variable amount of total motion against the embankment.

This physical analogy doesn't capture the memory of a memristor, so it is fundamentally flawed. But, hey - at least it's a start.

Originally posted by SO1OS:As such, because it is able to produce the linear behavior of a resistor with a constant current, I think it's a generalization and, as such, will replace it as a fundamental passive element. Still leaving the EE's with three, then.

Not exactly. The resistance is a function of net charge passed through the device, so a constant current will result in a changing resistance. An AC is required to keep the resistance "constant" if current is to pass through it.

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Hate to disagree, but the impact this'll have on FPGA/DSP (at the onset) will be enormous, assuming it can be integrated with Si.

I was addressing Dr. Chua's comment about changing V=IR. I don't doubt the miniaturization potential of this tech, even if Dr. Chua's mistaken.